Let,
z1=x1+iy1 and z2=x2+iy2
∵Re(z1z2)=0
x1x2−y1y2=0......(i)
∵Re(z1+z2)=0
x1+x2=0......(ii)
From equations (i) and (ii) we get
x12+y1y2=0
⇒y1y2=−x12
Therefore Im(z1) and Im(z2) are of opposite sign
JEE Main 2023 — Mathematics Algebra
For two non-zero complex number z1 and z2, if Re(z1z2)=0 and Re(z1+z2)=0, then which of the following are possible?
(A) Im(z1)>0 and Im(z2)>0
(B) Im(z1)<0 and Im(z2)>0
(C) Im(z1)>0 and Im(z2)<0
(D) Im(z1)<0 and Im(z2)<0
Choose the correct answer from the options given below:
Held on 29 Jan 2023 · Verified 6 Jul 2026.
B and D
B and C
A and B
A and C
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